<p>A new kinetic theory for free radical copolymerization with long chain branching and crosslinking is proposed. This kinetic theory accounts for the history of the generated network structure as well as for all of the important elementary reactions in free radical polymerization. The present theory can be used to make calculations of various important properties such as onset of gelation, weight fraction of sol and gel, number- and weight-average chain length of sol fractions, crosslinking density in sol and gel fractions, etc. Since free radical polymerization is kinetically controlled, each primary polymer molecule experiences a different history of crosslinking and cyclization. The present theory proves the existence and permits the calculation of the crosslinking density distribution, although all statistical models which assume an equilibrium system inevitably employ the assumption that the crosslinking density is the same for all chains. The existence of a crosslinking density distribution with a significant variance is an important feature of the present kinetic theory stating that polymer networks synthesized by free radical polymerization are inherently inhomogeneous on a microscopic scale. This theory reduces to the Flory/Stockmayer theory under Flory's simplifying assumptions and may therefore be considered a general mean-field theory.</p> <p>The present theory was successfully applied to the copolymerization of methyl methacrylate/ethylene glycol dimethacrylate, and acrylamide/N,N'-methylene-bis-acrylamide. In real systems it was found that the effect of cyclization (intramolecular reactions) and the decreased reactivity of pendant double bonds relative to the monomeric double bonds are important.</p> <p>This new kinetic theory should assist one to design superior quality network polymer systems and it can also be used to control various polymerization processes. It was found that if branches are formed by chain transfer to polymer the crosslinking density is always higher in continuous stirred tank reactors (CSTR) than in batch reactors, however, this is not true in general for vinyl/divinyl copolymerizations. The variance of the crosslinking density distribution in CSTR's is large due to their broad residence time distributions.</p> / Doctor of Philosophy (PhD)

<p>The present research investigates, both theoretically and experimentally, transport phenomena in reverse osmosis (RO) membranes.</p> <p>In order to properly describe and predict RO membrane performance, and to properly design RO units, a good understanding of the fundamentals of the membrane transport is needed; this means that a strong transport model needs to be developed. This research is concerned with the development of such a model. As well, the effects of system pressure, concentration, and temperature on the performance of thin-film composite, aromatic polyamide RO membranes with sodium chloride and some other salts are examined both experimentally and theoretically.</p> <p>The present research investigates the development of a powerful, novel transport model for reverse osmosis, which does not have the serious shortcomings of the previous models, and an experimental evaluation of this model. As a result, a mechanistic model, called the Modified Surface Force-Pore Flow (MD-SF-PF) model, has been developed. The model assumes that transport through the membrane takes place in very fine pores, and the pores are modeled as perfect cylinders. In this two-dimensional model, a balance of applied and frictional forces acting on the solute in a pore is given as a function of radial and axial positions. The model incorporates a potential field inside the membrane which is responsible for the partitioning effect (at the two sides of the membrane) and, in part, determines the membrane performance. A computer code has been developed, based on the "orthogonal collocation" method of weighted residuals, which has proven to be very efficient and precise to solve the complicated differential equations of the transport models.</p> <p>Three models have been developed during the present research: i) the Modified Surface Force- Pore Flow (MD-SF-PF) model, briefly described above, which is appropriate for solvent-membrane affinity systems (such as salt-water systems); a temperature-extended version of this model has also been derived; ii) the Extended MD-SF-PF model (a generalized form of the MD-SF-PF model) which can be used to describe or predict any type of RO system, that is, both solvent-membrane affinity systems, such as sodium chloride-water system, and solute-membrane affinity systems, such as toluene-water system; and iii) the Modified Finely Porous Model (MD-FPM) which is a one-dimensional transport model, and can describe simple systems.</p> <p>Experimental data are used to determine model parameters. Also, experimental data can be compared to model predictions. The following experimental plan was undertaken using aromatic polyamide (FilmTec) FT30 membranes: i) experiments with 2000 ppm aqueous solutions of sodium chloride (brackish water concentration) in the range 350-7000 kPa and 5-60°C (a few experiments at 25°C and 5000, 10000, and 15000 ppm sodium chloride solutions were also performed (Phase I)); ii) experiments with 2000 ppm potassium chloride, lithium chloride, and lithium nitrate at 25°C and 500-4000 kPa (Phase II); and iii) experiments with 35 000 ppm sodium chloride (sea water concentration) at 4000-7000 kPa and 5-60°C (Phase III).</p> <p>Model parameters were determined from the data of Phase I at 25°C, using a nonlinear optimization routine. The average pore radii for the SW30HR and BW30 types of FT30 membranes were determined at about 1.0 and 1.2 nm, respectively. All the experimental data at other pressures and concentrations are well predicted by the MO-SF-PF model. Somewhat fortuitously, the MO-SF-PF model also predicts well for the other 1-1 electrolytes.</p> <p>Temperature effects are reasonably predicted by the temperature-extended MD-SF-PF model. The apparent activation energies for pure water permeability for the SW30HR and BW30 membranes are about 25400 and 22500 kJ/kmol at 5-40°C, respectively, and about 18100 and 13 000 kJ/kmol at 40-60°C, respectively. Compaction, which becomes more severe as temperature or pressure is increased, has no effect on predicting the membrane separation or flux ratio (the ratio of total solution flux to pure solvent flux). An empirical model for compaction has also been developed and used to correct the flux ratio to the absolute values of permeation fluxes.</p> <p>The Extended MD-SF-PF model has been found to well describe the difficult case of strong solute-membrane affinity, in which solute molecules are attracted toward the membrane rather than being rejected. The model implies that once the solute is rapidly sorbed into the membrane the solute molecules creep slowly adjacent to the wall of the membrane pores.</p> <p>Overall, the family of the MD-SF-PF models has been found to predict RO membrane performance over a wide range of operating conditions. The agreement between the experimental data and model predictions supports, but does not prove, the proposed transport mechanism. In principle, the family of the MD-SF-PF models can be used for different research purposes including membrane development and RO module design.</p> / Doctor of Philosophy (PhD)

<p>In this work which consists of two parts, two important aspects in latex production and in the control of latex reactors were studied: the determination of latex particle size using on-line and off-line measurements and the particle nucleation in emulsion polymerization in the absence of micelles.</p> <p>In the first part, three particle sizing methods (turbidimetry, dynamic light scattering and packed column chromatography) were evaluated for their capability to provide accurate estimates of the particle size distribution (PSD) and for their potential to be applied for on-line measurements to monitor and control the particle size in latex reactors. Dynamic light scattering was successfully applied on-line to follow particle growth during the emulsion polymerization of vinyl acetate in a pilot scale reactor. A layout for the hardware of an on-line sampling device which can be used with packed column chromatography is also suggested. Electron microscopy was used to corroborate results from these methods. Several interesting features were observed during this study and this motivated an in-depth investigation of some aspects related to these methods.</p> <p>A detailed theoretical and experimental investigation showed for the first time that turbidimetric methods are not expected to provide an estimate of the full PSD in certain cases, and identified these cases. Based on this analysis a controversy and several inconsistencies in the literature were resolved. It was also shown that the wavelength exponent and the turbidity ratio are not different but equivalent methods.</p> <p>In electron microscopy shrinkage of the latex particle under the electron beam was investigated. It was shown that the diameter decreases in an exponential manner with the time of exposure to the electron beam, and that the largest reduction occurred within the first minutes of exposure.</p> <p>For the packed column chromatography method, software was developed for the conversion of the observed chromatogram to PSD. This software allows for a retention volume dependent spreading function, mass or turbidity detector and extinction coefficient calculations by taking into account the refractive index of the particles. A chromatographic apparatus operating with two detectors (turbidity and differential refractometer) connected in series was utilized to monitor particle growth during the reaction.</p> <p>In the second part a systematic study of the emulsion polymerization of vinyl acetate in the absence of soap micelles in a pilot plant reactor was carried out. The effects of several variables on the particle size and the reaction rate were investigated in a series of designed experiments. These parameters were: initiator and monomer concentration, monomer and water soluble impurities and agitation. Both soap free runs and runs with soap concentrations much below the CMC were included in the design. Even though the objective was a systematic study of the soap free polymerization of vinyl acetate, the experiments with soap levels below the CMC were included to provide additional data in an attempt to reconcile the conclusions derived from experiments carried out with no soap and with soap levels above CMC. To test for the reliability and the reproducibility of the results some of the polymerization runs were repeated. Most of the measurements were duplicated or triplicated and the particle size was determined with 3 different methods.</p> <p>Accurate and reproducible data were obtained. The results were consistent, at all levels of the parameters, both in the soap free polymerizations and in the runs with soap below CMS. These results help to clarify certain mechanisms, and to link phenomena observed in the soap free cases with those in polymerizations with soap above CMC, and to understand the similarities and differences. This set of data can offer valuable information for the modelling of several mechanisms of the homogeneous nucleation.</p> / Doctor of Philosophy (PhD)

<p>This thesis presents new results in the research area of multiple input/multiple output(MIMO) controller design for chemical processes. The topics considered in this work are: robustness properties of linear MIMO controller designs; the design of approximate inverses for linear MIMO controllers; disturbance prediction in model predictive controller designs; and the development of a nonlinear inferential feedback control strategy for semi-batch copolymerization processes.</p> <p>A review of robustness analysis procedures based on the use of norm bounded mismatch regions in the frequency domain is presented. These theories are considered for use in the assessment of the relative robustness trends of different MIMO Internal Model Controller designs. Based on these theories, three approaches to analyzing robustness properties are considered: the use of a condition number and singular value analysis on the approximate model inverse; singular value analysis assuming unstructured norm bounded uncertainty; and new procedure based on disk uncertainties in each element of the transfer function matrix that requires the use of structured singular value theory. The problems of conservatism with each approach as a result of unrealistic uncertainty characterizations is discussed, and new results are provided. The approaches are compared and evaluated with different MIMO Internal model controller designs. Compared to previously proposed procedures for relative robustness assessment, new proposed procedure based on disk uncertainties in each element of the transfer is shown to reduce conservatism in analyzing controller design robustness trends.</p> <p>A general method for obtaining least squares optimal inverses for multivariable Internal Model Controllers (IMCs) is presented. An analytical solution is arrived at using a well known method for optimally factorizing discrete transfer function matrices. The procedure automatically handles unbalanced, noninvertible, and nonsquare systems, and provides controllers with excellent performance and robustness properties. These IMC designs are compared with some of the more traditional IMC designs where tunable diagonal filters are combined with fixed but usually suboptimal inverses. Robustness properties are investigated in simulated mismatch case studies, and with the robustness assessment procedures described above.</p> <p>A general procedure is proposed for improving disturbance regulation in MlMO Dynamic Matrix Controllers (DMC). The method makes use of autoregressive, integrated moving average disturbance models to provide disturbance predictions, and requires only a simple modification to the DMC algorithm. The method proposed is far more computationally efficient and simple to apply relative to other procedures proposed. Examples are presented were the proposed modification leads to a substantial improvement in DMC disturbance regulation.</p> <p>A strategy is proposed for estimating and controlling properties of styrene/butadiene rubber (SBR) latex produced in a semi-batch reactor. The nonlinear control strategy features a nonlinear state estimator, a nonlinear open-loop feedforward compensator, and a linear feedback controller to correct for errors in the feedforward control actions. In arriving at a nonlinear state estimator, three approaches, extended Kalman filtering, extended Kalman filtering with global reiteration, and a nonlinear optimization approach were considered. The second approach was found to be most effective and was therefore adopted. The importance of introducing sufficient meaningful nonstationary states is discussed in order to have biased-free state estimates when nonideal conditions exist. Using the knowledge of modelled chemical reaction mechanisms, open-loop feedforward actions are proposed based on establishing conditions for maintaining fixed instantaneous copolymer properties. These open-loop/feedforward policies establish quasi-steady state conditions on the instantaneous copolymer properties to be controlled. This allows for the application of simple feedback control strategies to correct for errors remaining after the open-loop/feedforward actions. The approaches considered for feedback controller design were conventional paired PI, a decoupling and linearizing mullivariable transfonnation approach, and model-based optimal controller design. The second approach was found to be the most convenient for use in the nonlinear inferential feedback control scheme. The performance of the overall nonlinear inferential feedback design strategy proposed in this work is demonstrated to be robust to model mismatch, disturbances, and state initialization errors. In all cases investigated, copolymer properly control is greatly improved over a fixed operating policy determined off-line. The proposed strategy is simple and effective alternative to computationally intensive on-line optimization procedures, and has the potential for greatly improving product reproducibility and quality control in polymer manufacturing industries.</p> / Doctor of Philosophy (PhD)

<p>The mechanism of the free radical polymerization of acrylic water soluble monomers has been elucidated. Donor-acceptor interactions between initiator and monomer form a weak charge transfer complex which acts as a secondary source of initiation. This accounts for the unusually high rate dependence on monomer concentration observed for nonionic, anionic and cationic monomers. In polymerizations where the initiator and monomer are segregated, as for example in inverse-microsuspension, monomer enhanced decomposition is absent. Three other reactions dominate: unimolecular chain termination with interfacial emulsifier, heterophase diffusion of primary and oligoradicals and long chain branching with unsaturated carbons on the terminal oleate groups.</p> <p>A new light scattering procedure has been developed based on the theoretical prediction of the second virial coefficient. The method eliminates greater than fifty percent of the variance in estimation of molecular weight, concomitant with a fivefold reduction in measurement time, and can be applied to any linear polymer, including polyelectrolytes.</p> / Doctor of Philosophy (PhD)

<p>Methanol and higher alcohols are produced when mixtures of CO, CO₂ and H₂ are reacted over Cu/ZnO catalysts at temperatures above about 250°C and pressures of 5 to 10 MPa. Relatively little is known about the synthesis of this mixed alcohol product, which has potential usefulness as a liquid fuel, or as a non-lead octane improver for gasoline. In the present work, various aspects of the synthesis of methanol and higher alcohols over Cu/ZnO/Cr₂O₃ catalysts have been investigated.</p> <p>Addition of ¹³C labelled methanol to the reactor feed gas showed that methanol is incorporated directly into the higher alcohol product. Enrichment patterns of ¹³C in the higher alcohols suggested that CO is also a direct precursor of C₁ intermediates which produce higher alcohols.</p> <p>A kinetic model of the higher alcohol synthesis (HAS), derived on the basis of direct mechanistic information, has not been reported. In the present work, the kinetics of the HAS have been successfully modelled by a scheme in which CH₃OH, CO, and CO₂ are converted directly into higher alcohols. The model was found to be consistent with the kinetic observations made for a wide range of reactor operating conditions including: H₂/(CO+CO₂) ratios of 0.36 to 1.8, CO₂/CO ratios of 0 to 1.35, CH₃OH feed concentrations of 0 to 5.3 percent, for (CO+H₂) conversions of 3.5 to 18 percent and at total pressures ranging from 5 to 10 MPa.</p> <p>The kinetic observations of the methanol synthesis, made under the same operating conditions, were well described by a model based on the assumption that methanol is formed from both CO and CO₂ in parallel reactions, on different catalytic sites. This model is unique in that it is consistent with the most recent mechanistic and kinetic observations of other workers, and in that it describes the methanol synthesis behaviour at conditions suitable for the HAS.</p> <p>Similarities between the methanol and higher alcohol synthesis models suggest that sites which convert CO to methanol also convert CO to higher alcohols, while sites that convert CO₂ to methanol also convert CO₂ to higher alcohols. Experiments with catalysts promoted with various amounts of K₂CO₃ promoter suggest that CO conversion is associated with alkali sites or alkali/copper interfaces, while CO₂ conversion is associated with unpromoted copper sites. This view reconciles many apparently contradictory results which have been reported in the literature.</p> / Doctor of Philosophy (PhD)

<p>Linear polymers, copolymers, microgels and macrogels based on N -isopropylacrylamide were prepared and the properties of these materials at the air/water interface were investigated. Dynamic surface tensions were measured by pendent drop experiments in which either the drop volumes were constant or were oscillated. The ability of colloidal microgels to lower surface tension is unusual and, for the first time, Environmental Scanning Electron Microscopy provided images showing an ordered array of 500 nm diameter microgels adsorbed at the air/water interface. The surface tension of poly(N -isopropylacrylamide) homopolymers and microgels was about 43 mJ/m2 at 25°C, and surface tension decreased slightly with increasing temperature between 25∼40°C. The temperature insensitivity of surface tension is remarkable because in solution the linear polymer phase separated and the microgel were dehydrated when the temperature was raised from 25 to near 40°C. The introduction of hydrophilic acrylamide moieties increased surface tension and the results were fit to a one-parameter model analogous to the Margules model for the fire energy of mixing of solutions. Kinetic models were developed and fitted to the dynamic surface tension data. A key challenge was relating surface tension to the amount of adsorbed material at the interface. Results are shown for calculations based on both published data and statistical mechanical models of adsorbed polymer. The inability of mass transport models to predict the kinetics suggested that rearrangement of gels or linear polymer at the interface contributed to the kinetics. Macroscopic water swollen gels like the linear polymers and the microgels displayed a low surface energy due to the accumulation of isopropyl groups at the interface. However, unlike the microgels and linear polymers, the surface characteristics reflected in contact angle measurements was sensitive to temperature in the critical range 35 to 40°C.</p> / Doctor of Philosophy (PhD)

<p>A horizontal configuration for a pulsed solvent extraction contactor has been recognized as having a great potential in replacing standard vertical pulsed columns (VPC) in the separation of heavy elements in the reprocessing of spent nuclear fuel. Published work examining the performance of the horizontal pulsed column (HPC) has been sparse to date, thus preventing the design of large-scale units.</p> <p>The hydrodynamic studies were conducted in a 0.072-m by 1-m long column with a perforated-plate cartridge arrangement using a 30% tributyl phosphate +70% Isopar M -2.0 mol/L nitric acid system. The hydrodynamic behaviour was characterized in terms of throughput capacity, dispersed phase holdup, axial mixing of both phases and power dissipation. Emphasis in this study was given to the effects of the major operating variables that include: aqueous and organic flowrates, and pulse amplitude and frequency, on the key hydrodynamic factors. The effects of physical properties for liquid-liquid systems and plate geometry were also examined for selected hydrodynamic factors.</p> <p>The variation of throughput capacity with the operating variables was found to be similar to that reported for the VPC when presented on standard flooding diagrams. The flooding behaviour of the HPC was strongly dependent on both pulse amplitude and frequency, as well as on the coupled pulse effect represented by pulse velocity. A procedure for constructing flooding diagrams from correlations derived from experimental results was demonstrated. Mechanisms to determine the onset of flooding and flooding anomalies were investigated and the results compared with experimental data.</p> <p>A detailed analysis of the dispersed (aqueous) phase holdup was made. The aqueous holdup did not vary significantly along the column, however, local radial variations are reported. Correlations based on experimental data for the average holdup for the HPC indicated the effect of the major operating variables is similar to that reported for the VPC in the mixer-settler region of operation. However, the range of the aqueous holdup observed for the HPC (0.15 - 0.50) is several times larger than that typically reported for the VPC.</p> <p>Axial mixing, as determined by a two-point tracer method of measurement, was well represented by a backflow model. Axial mixing of the dispersed (aqueous) phase was found to be insignificant. The organic phase axial mixing was significant with backflow coefficients as large as 25.4 (dispersion coefficient of 18.2 cm²/s) were observed. The effects of the major operating variables on the organic phase axial mixing in the HPC were consistent with similar data reported for the VPC.</p> <p>Power dissipation studies, by the force-displacement method, revealed a pronounced dependency on the pulse amplitude-frequency product. Individual phase flowrates were found to have a minimal effect on the time-averaged power dissipation. Experimental results were in good agreement with a quasi-steady state model commonly used for the VPC.</p> <p>A comparison of the major hydrodynamic factors for the HPC with the VPC suggested that the HPC can be a viable alternative where space and portability factors are critical.</p> / Doctor of Philosophy (PhD)

<p>The effects of operating variables of red mud deep thickening have been examined. The independent (operating) variables studied were 1) The dosage of an anionic polymeric flocculant and 2) the solids throughput. The dependent variables were the concentration of underflow solids, underflow withdrawal rate, overflow rate, overflow quality and steady state solids concentration profile.</p> <p>The major effect of the flocculant dose was an increase in the separation efficiency (a measure of the degree of thickening) for an increase of flocculant dose.</p> <p>The solids concentration profiles obtained showed that the majority of the thickening of the mud occurred in the bottom fifth of the column. Therefore, for a given thickener and mud type, there exists a certain bed depth above which no substantial gain in separation efficiency is achieved.</p> <p>When all other variables are the same, the column diameter-to-length ratio and operational temperature had the most significant effect on the separation efficiency.</p> / Master of Engineering (ME)

<p>Flow phenomena associated with die extrusion and coextrusion have a significant impact on the final product shape and layer uniformity. The present work is concerned with the mathematical modelling and numerical simulation of three dimensional single-component and stratified multi-component extrusion. The objective is to provide an understanding of the flow phenomena involved and investigate their impact on the shape and interface configuration of the extruded article.</p> <p>A three dimensional non-isothermal study of viscous free-surface flows with exponential dependence of viscosity on temperature is presented. The effects of non-isothermal conditions and/or geometry on the extrudate shape are investigated with a fully three dimensional finite element/Galerkin formulation. Special free surface update schemes (pathline, spine and hybrid spine/pathline methods) are presented and enable the study of the extrudate swelling out of very complicated 3-D geometric shapes. Apart from the well known thermally induced extrudate swelling phenomenon, bending and distortion of the extrudate may occur because of temperature differences and/or geometric asymmetries. A temperature difference across the die can be imposed by heating or cooling the die walls, but can also arise because of asymmetric viscous heat generation due to the die geometry. Temperature differences affect velocity profiles because of the temperature dependence of viscosity and lead to extrudate bending and distortion. It is also shown numerically and confirmed experimentally that the die geometry can induce extrudate bending even in the case of isothermal Newtonian flows.</p> <p>A powerful finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (interface, external free surfaces) is tackled with advanced free surface update schemes. The pressure and viscous stress discontinuity at the interface occurring because of the viscosity mismatch is handled with both a double node (u-v-w-P₁-P₂-h₁-h₂) formulation and a penalty function (u-v-w-P-h₁-h₂) formulation.</p> <p>The interface shape development and extrudate swelling behaviour of stratified flows in a sheath- core configuration is examined. The viscosity mismatch has an effect on both the interface and the external free surface shapes. The flowrate ratio, die geometry and layer configuration are also shown to affect the areas of flow of the individual layers and the extrudate swelling behaviour of the bicomponent system.</p> <p>The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of a side-by-side configuration is established with the aid of both a fully 3-D analysis and a 1-D optimization analysis, in agreement with experimental evidence. It is shown that the direction and degree of encapsulation depend directly on the viscosity ratio. For shear thinning fluids exhibiting a viscosity crossover point, interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. The effects of the length of flow and slip at the wall on the degree of encapsulation are investigated. The effect of initial conditions and design of the layer merging part on the interface shape development downstream is also examined and potential sources of instabilities are identified. The extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is also shown.</p> / Doctor of Philosophy (PhD)